Existence of solutions for the p-Laplacian with critical Sobolev exponent and convection

References

• Brézis , H and Nirenberg , L . 1983 . Positive solutions of nonlinear elliptic equations involving critical Sobolev exponents . Comm. Pure Appl. Math. , 36 : 437 – 477 .
   Web of Science ®Google Scholar
• Zhu , XP . 1988 . Nontrivial solution of quasilinear elliptic equations involving critical Sobolev exponent . Sci. Sinica Ser. A , 31 : 1166 – 1181 .
   Google Scholar
• Guedda , M and Veron , L . 1989 . Quasilinear elliptic equations involving critical Sobolev exponents . Nonlinear Anal. , 13 : 879 – 902 .
   Web of Science ®Google Scholar
• Escobar , JF . 1987 . Positive solutions for some semilinear elliptic equations with critical Sobolev exponents . Comm. Pure Appl. Math. , 40 : 623 – 657 .
   Google Scholar
• Egnell , H . 1988 . Semilinear elliptic equations involving critical Sobolev exponents . Arch. Rational Mech. Anal. , 104 : 27 – 56 .
   Google Scholar
• Egnell , H . 1988 . Existence and nonexistence results for m-Laplace equations involving critical Sobolev exponents . Arch. Rational Mech. Anal. , 104 : 57 – 77 .
   Web of Science ®Google Scholar
• Grossi , M . 1991 . Existence and multiplicity results in the presence of symmetry for elliptic equations with critical Sobolev exponent . Nonlinear Anal. , 17 : 973 – 989 .
   Google Scholar
• Wei , ZH and Wu , XM . 1992 . A multiplicity result for quasilinear elliptic equations involving critical sobolev exponents . Nonlinear Anal. , 18 : 559 – 567 .
   Web of Science ®Google Scholar
• Sang , JY . 1994 . Multiplicity results and bifurcation for nonlinear elliptic problems involving critical Sobolev exponents . Nonlinear Anal. , 23 : 1493 – 1498 .
   Google Scholar
• Cao , DM and Zhong , X . 1997 . Multiplicity of positive solutions for semilinear elliptic equations involving the critical sobolev exponents . Nonlinear Anal. , 29 : 461 – 483 .
   Google Scholar
• Drábek , P and Huang , YX . 1997 . Multiplicity of positive solutions for some quasilinear elliptic equation in ℝ N with critical Sobolev exponent . J. Differ. Eqns , 140 : 106 – 132 .
   Web of Science ®Google Scholar
• Silva , EAB and Xavier , MS . 2003 . Multiplicity of solutions for quasilinear elliptic problems involving critical Sobolev exponents . Ann. Inst. H. Poincaré Anal. Non-linéaire , 20 : 341 – 358 .
   Google Scholar
• Han , PG and Liu , ZX . 2004 . Multiple positive solutions of strongly indefinite systems with critical Sobolev exponents and data that change sign . Nonlinear Anal. , 58 : 229 – 243 .
   Web of Science ®Google Scholar
• Cao , DM and Han , PG . 2004 . Multiple positive solutions of nonhomogeneous elliptic systems with strongly indefinite structure and critical Sobolev exponents . J. Math. Anal. Appl. , 289 : 200 – 215 .
   Web of Science ®Google Scholar
• Huang , YS . 1999 . On Multiple solutions of quasilinear equations involving the critical Sobolev exponent . J. Math. Anal. Appl. , 231 : 142 – 160 .
   Google Scholar
• Cerami , G , Fortunato , D and Struwe , M . 1984 . Bifurcation and multiplicity results for nonlinear elliptic problems involving critical Sobolev exponents . Ann. Inst. H. Poincaré Anal. Non-linéaire , 1 : 341 – 350 .
   Web of Science ®Google Scholar
• Azorero , JG and Alonso , IP . 1991 . Multiplicity of solutions for elliptic problems with critical exponent or with a nonsymmetric term . Trans. Amer. Math. Soc. , 323 : 877 – 895 .
   Web of Science ®Google Scholar
• Chhetri , M , Drábek , P , Raynor , S and Robinson , S . 2008 . Nonvariational problems with critical growth . Nonlinear Anal. , 68 : 2092 – 2103 .
   Google Scholar
• Browder , FE . 1970 . Nonlinear elliptic boundary value problems and the generalized topological degree . Bull. Amer. Math. Soc. , 76 : 999 – 1005 .
   Google Scholar
• Berkovits , J . 2007 . Extension of the Leray–Schauder degree for abstract Hammerstein-type mappings . J. Differ. Eqns , 234 : 289 – 310 .
   Web of Science ®Google Scholar
• Damascelli , L . 1998 . Comparison theorems for some quasilinear degenerate elliptic operators and applications to symmetry and monotonicity results . Ann. Inst. H. Poincaré , 15 : 493 – 516 .
   Google Scholar
• Guo , DJ . 2004 . Nonlinear Functional Analysis , Ji'nan : ShanDong Science and Technology Press .
   Google Scholar
• Brezis , H and Lieb , E . 1983 . A relation between pointwise convergence of functions and convergence of functionals . Proc. Amer. Math. Soc. , 88 : 486 – 490 .
   Web of Science ®Google Scholar
• Flucher , M . 1999 . Variational Problems with Concentration , Basel : Birkhäuser .
   Google Scholar